We show that most homogeneous Anosov actions of higher rank Abelian groups are locally
smoothly rigid (up to an automorphism). This result is the main part in the proof of local …

This self-contained monograph presents rigidity theory for a large class of dynamical
systems, differentiable higher rank hyperbolic and partially hyperbolic actions. This first …

Publisher Summary This chapter discusses the case of group, as opposed to semi-group,
actions. There are various technical complications that arise in passing from invertible to …

The first part of the paper begins with an introduction into Anosov actions of Zfc and Mk and
an overview of the method of studying invariant measures for such actions based on …

Under some weak hyperbolicity conditions, we establish C^ 0-and C^\infty-local rigidity
theorems for two classes of standard algebraic actions:(1) left translation actions of higher …

ON THE CLASSIFICATION OF CARTAN ACTIONS Boris Kalinin and Ralf Spatzier 1
Introduction Page 1 GAFA, Geom. funct. anal. Vol. 17 (2007) 468 – 490 1016-443X/07/020468-23 …

This paper contains a collection of open problems from the the workshop “Emerging
applications of measure rigidity” held at the American Institute of Mathematics in June, 2004 …

This text is an expanded series of lecture notes based on a 5-hour course given at the
workshop entitled" Workshop for young researchers: Groups acting on manifolds" held in …

In this article we prove global rigidity results for hyperbolic actions of higher-rank lattices.
Suppose Γ is a lattice in a semisimple Lie group, all of whose factors have rank 2 or higher …

This survey is dedicated to Professor Anatole Katok on the occasion of his sixtieth birthday.
He has made numerous important contributions to dynamics and ergodic theory proper …